Fourier transformation can improve quadrature efficiency of Laplace distribution

by Jinhyo Kim and Sangwon Seo .

Abstract: A numerical quadrature of a particular probability integral is concerned with using the Fourier transformation which smoothes the stiffness. \ The Fourier transformation of the Laplace distribution becomes, in a statistical sense, the Cauchy distribution. \ It is shown that the Gauss-Hermite quadrature of the Cauchy distribution, equivalent to the {\em Fourier-transformed} Laplace distribution, exhibits {\em better numerical} efficiency than the Gauss-Hermite quadrature of the {\em untransformed} Laplace distribution. \ A numerical example supports the analytic argument.

Key Words: Fourier transformation, Gauss-Hermite quadrature, Laplace distribution, Cauchy distribution

Authors:
Jinhyo Kim , jinkim@stats.snu.ac.kr
Sangwon Seo, sangwon@math.snu.ac.kr

Editor: John P. Hinde , J.P.Hinde@exeter.ac.uk

READING THE ARTICLE: You can read the article in portable document (.pdf) format (201021 bytes.)

NOTE: The content of this article is the intellectual property of the authors, who retains all rights to future publication.

This page has been accessed 3019 times since July 24, 2006.


Return to the InterStat Home Page.